Thirdly. If the body can be moved so rapidly that the fluid cannot instantaneously press in behind it, as is found to be the case in the atmosphere, the resisting power of the medium must be considerably increased, for the projectile being deprived of the pressure of the fluid on its hind part, must support on its fore part the whole weight of a column of the fluid, over and above the force employed in moving the portion of the fluid in contact with it, which force is the sole source of resistance in the discontinued fluid. Also, the condensation of the air in front of the body will influence considerably the relation between the resistances and the velocities of an oblique surface: and it is highly probable that although the resistances to a globe may for slow motions be nearly proportional to the squares of the velocities, they will for great velocities increase in a much higher ratio. ON THE VELOCITY WITH WHICH AIR WILL RUSH INTO A VACUUM. ~The velocity of the rush of air into a vacuum.~ When considering the resistance of the air to a body in motion, it is important that the velocity with which air will rush into a vacuum should be determined; and this will depend upon its pressure or elasticity. ~Result.~ It has been calculated, that air will rush into a vacuum at the rate of about 1,344 feet per second when the barometer stands at 30 inches, so that should a projectile be moving through the atmosphere at a greater velocity than this, say 1,600 feet per second, then would there be a vacuum formed behind the ball, and instead of having merely the resistance due to the inertia of the particles of the air, it would, in addition, suffer that from the whole pressure of a column of the medium, equal to that indicated by the barometer. UPON THE RESISTANCE OF THE AIR TO BODIES OF DIFFERENT FORMS. ~Difficulties of the question.~ The influence of the form of a body upon the resistance offered to it by a fluid, is a problem of the greatest difficulty; and although the most celebrated mathematicians have turned their attention to the subject, still, even for slow motions, they have only been able to frame strictly empirical formula, founded upon the data derived from practice; while with regard to the resistance at very high velocities, such as we have to deal with, very little light has hitherto been thrown upon the subject. ~Compressed fluid.~